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Observing the effects of changing tox to the gain of a simple amplifier

Observing the effects of changing tox to the gain of a simple amplifier. By R. E. Evans. tox. Process parameter Thickness of the gate oxide Cox = εox/tox -> As tox increases, Cox decreases Cox affects ß, gate capacitance. Why vary tox?. Because fabrication process is not perfect

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Observing the effects of changing tox to the gain of a simple amplifier

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  1. Observing the effects of changing tox to the gain of a simple amplifier By R. E. Evans

  2. tox • Process parameter • Thickness of the gate oxide • Cox = εox/tox -> As tox increases, Cox decreases • Cox affects ß, gate capacitance

  3. Why vary tox? • Because fabrication process is not perfect • Variation in tox will vary from wafer to wafer and slight variation on the same platter • This experiment varies tox beyond tolerances to make the results look good, but the same experiment can be done with actual variations from a given process and foundry which usually go between 0.1nm to 1nm

  4. My experiment • Make a schematic of a simple amplifier • Alter the sized pair model to allow for variation of tox • Use previous test circuits to find gm, gds • Find an equation for gain in terms of tox • Show theoretical versus simulated

  5. Simple amplifier circuit

  6. Simulation parameters • Changed TOX to TOX = {tox + 1.41E-8} • Will vary tox from -7nm to 49 nm in 7nm steps • Sweep Vin from 0 to 2 volts, Ix = 100 uA

  7. Results • Gain = -gm1/(gds1+gds2) • gm is in terms of beta, which is dependent on Cox, which is dependent on tox • Use our level-1 approximation for gm1, gds1, gds2 • gds1 = I+Ino/Va gds2=I+Ipo/Va gm1=SQRT(2*eox/tox*uo*W/L*(I+I1))

  8. Results - Gain

  9. Results – Max Gain vs. Tox

  10. Results – Max Gain vs. Tox from -1nm to +1nm

  11. Results – gds1, gds2, gm1 • From previous exercises: gds1 = 3.68 V, gds2 = 6.4 V • gm1 = SQRT(B*(100+45)) • Theoretical gain = -SQRT(2*0.6*B*(100+45))/(3.68+6.4)

  12. Curve Fit • Difference between my theoretical values and simulated values were off by a small factor • Added a shift element to the equation • New Theoretical gain = -SQRT(2*0.6*B*(100+45))/(3.68+6.4)*-12

  13. Results - Curve

  14. Conclusion • Saw the overall effect of changing tox, did get my expected results: which means I had a good equations and tox vs. gain can be modeled in level-1 terms • Reported tolerances in tox can shift the peak gain by 6 which needs to be at least noted when designing analog IC’s

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